To borrow a phrase, impeaching Donald Trump offers a target rich environment. Any inquiry has to have a starting point and a specific set of questions, which are pretty obvious when the inquiry is reasons to impeach Donald Trump.
Obstruction of Justice is an obvious choice, but there are so many to choose from, it only makes sense to dive in and see which lines of inquiry prove most fructive.
Michael Cohen handed the House another issue, violation of election laws. Cohen has already pleaded guilty to multiple crimes that offer an array of possible other crime that Trump himself committed. He pleaded guilty because federal prosecutors raided his office and two domiciles, carting off enough documents, apparently, plenty of information to corner him.
If they cornered Cohen, they can corner the president. The FBI still operates under the Department of Justice, so Barr would likely try to stop them from handing over the evidence, but that is just more of the same. There may be other ways to get that evidence. Cohen may have violated state laws such that state agencies have relevant evidence as well. Cohen can come testify.
This is not hard. Get creative. Impeach.